- #1

- 40

- 4

- Homework Statement
- Finding out relevant equation for work done on a dipole and its potential energy.

- Relevant Equations
- $$ W= -\Delta U $$

$$ U= -PEsin\theta $$

I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help.

The torque on a dipole can be defined as

τ=PEsinθ

The work done on a dipole to move it from an angle ##\theta_0## to an angle ##\theta_1## can be written as the integral of ##\tau.dr## from ##\theta_0## to ##\theta_1##

which is PE[cos##\theta_0##- ##\theta_1## ]

The change in potential energy would be ##U_2 -U_1##

=##-PEcos\theta_1## -(-##PEcos\theta_0##)

=##PEcos\theta_0##- ##PEcos\theta_1##

=PE[cos##\theta_0##- ##\theta_1## ]

If we compare the equations obtained for work done and the change in potential they both are the same which make sense since the change in potential energy would be the work done.

But this is where my problem begins. Isn't the work done negative of the change in potential energy due to a conservative force?

If yes why is ##W= \Delta U## here and not ##W= -\Delta U##

I know this sound silly but does it make a difference?

I have encountered problems with multiple choices where the sign mattered and wasn't sure which one to choose.

The torque on a dipole can be defined as

τ=PEsinθ

The work done on a dipole to move it from an angle ##\theta_0## to an angle ##\theta_1## can be written as the integral of ##\tau.dr## from ##\theta_0## to ##\theta_1##

which is PE[cos##\theta_0##- ##\theta_1## ]

The change in potential energy would be ##U_2 -U_1##

=##-PEcos\theta_1## -(-##PEcos\theta_0##)

=##PEcos\theta_0##- ##PEcos\theta_1##

=PE[cos##\theta_0##- ##\theta_1## ]

If we compare the equations obtained for work done and the change in potential they both are the same which make sense since the change in potential energy would be the work done.

But this is where my problem begins. Isn't the work done negative of the change in potential energy due to a conservative force?

If yes why is ##W= \Delta U## here and not ##W= -\Delta U##

I know this sound silly but does it make a difference?

I have encountered problems with multiple choices where the sign mattered and wasn't sure which one to choose.